The Approximate Capacity of Half-Duplex Line Networks

This paper investigates the problem of characterizing the capacity of Half-Duplex (HD) line networks, where a source node communicates to a destination node through a multihop path of N relays. If the relays operate in Full-Duplex (FD), it is well known that the capacity of the line network equals the minimum among the point-to-point link capacities in the path. In contrast, this paper considers a different case where the relays operate in HD. In the first part of the paper, it is shown that the approximate capacity (optimal up to a constant additive gap that only depends on the number of nodes in the network) of an HD N-relay line network equals half the minimum of the harmonic means of the point-to-point link capacities of each two consecutive links in the path. It is then proved that the N +1 listen/transmit states (out of the 2
^N
possible ones) sufficient to characterize the approximate capacity can be found in linear time. In the second part of the paper, it is shown that the problem of finding the path that has the largest HD approximate capacity in a network that can be represented as a graph is NP-hard. However, if the number of cycles in the network is polynomial in the number of nodes, then a polynomial-time algorithm can indeed be designed.